Does i = ℵ1 imply a = ℵ1?

Ascertain whether the independence number i equal to ℵ1 implies the almost disjointness number a equals ℵ1, i.e., determine if ZFC proves that i = ℵ1 ⇒ a = ℵ1.

Background

The independence number i and the almost disjointness number a are classical invariants of the continuum, and tight implications between their values at ℵ1 are not known. This question probes whether small i forces small a.

The notes emphasize that even this specific implication is not known, underscoring a key gap in our understanding of the structure of cardinal characteristics.